Simplify. \( (E \times x)^{-} 49^{-\frac{5}{4}} \cdot 49^{\frac{3}{4}} \)

To simplify the expression \( (E \times x)^{-} 49^{-\frac{5}{4}} \cdot 49^{\frac{3}{4}} \), we start by combining the powers of \( 49 \): \[ 49^{-\frac{5}{4}} \cdot 49^{\frac{3}{4}} = 49^{-\frac{5}{4} + \frac{3}{4}} = 49^{-\frac{2}{4}} = 49^{-\frac{1}{2}}. \] Next, we rewrite \( 49^{-\frac{1}{2}} \). Since \( 49 = 7^2 \), we have: \[ 49^{-\frac{1}{2}} = (7^2)^{-\frac{1}{2}} = 7^{-1} = \frac{1}{7}. \] Now, putting it all together with the factor \( (E \times x)^{-} \): \[ (E \times x)^{-} \cdot 49^{-\frac{5}{4}} \cdot 49^{\frac{3}{4}} = (E \times x)^{-} \cdot \frac{1}{7}. \] Hence, the final simplified expression is: \[ \frac{1}{7(E \times x)}. \]